Question 1

A researcher wants to estimate the proportion of college students who own a laptop. She surveys 200 students and finds that 160 own a laptop. Which formula should she use to calculate the standard error for the sample proportion?

Accepted Answer

$$SE(proportions) = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 2

Which of the following best describes the difference between an observational study and an experiment?

Accepted Answer

In an experiment, researchers actively assign treatments to subjects, while in an observational study, they only observe without intervention.

Question 3

A boxplot of test scores shows a minimum of 50, Q1 of 60, median of 70, Q3 of 80, and maximum of 100. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q3 - Q1 = 80 - 60 = 20$$

Question 4

A sample of 10 patients has cholesterol levels: 180, 190, 200, 210, 220, 230, 240, 250, 260, 270. What is the sample standard deviation?

Accepted Answer

$$s = \sqrt{\frac{\sum (x - \bar{x})^2$}{n-1}}$$

Question 5

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. What does this value indicate?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam scores.

Question 6

If a dataset is skewed right, which measure of center is likely to be greater?

Accepted Answer

The mean is likely to be greater than the median.

Question 7

A medical test for a disease has a 95% sensitivity and 90% specificity. If a patient tests positive, what is the probability that they actually have the disease called?

Accepted Answer

Conditional probability

Question 8

A researcher wants to compare the mean blood pressure between two groups: those who exercise and those who do not. Which formula should be used to calculate the standard error for the difference in means?

Accepted Answer

$$SE(diff\ of\ means) = \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 9

In a binomial experiment with $$n = 20$$ trials and probability of success $$p = 0.3$$, which formula calculates the probability of exactly $$k$$ successes?

Accepted Answer

$$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$

Question 10

A confidence interval for a population proportion is calculated as $$\hat{p} \pm z \cdot SE. $$What does this interval represent?

Accepted Answer

The range of values likely to contain the true population proportion with a specified level of confidence.

Question 11

Which of the following is NOT an assumption for a one-sample t confidence interval for a population mean?

Accepted Answer

The sample size must be less than 30.

Question 12

A hypothesis test for a population proportion yields a p-value of 0.03. If the significance level is 0.05, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 13

Which formula is used to calculate the sample size needed for a desired margin of error $$E in a $$confidence interval for a proportion?

Accepted Answer

$$n = \hat{p}(1-\hat{p}) \left( \frac{z}{E} \$$right)^2$$

Question 14

In a two-sample t-test for independent population means, which null hypothesis is appropriate?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$

Question 15

A study comparing two treatments uses the same subjects for both treatments. What type of samples are these?

Accepted Answer

Dependent samples

Question 16

If two events are mutually exclusive, what is the probability that both occur?

Accepted Answer

$$P(A 	ext{ and } B) = 0$$

Question 17

A z-score is calculated as $$z = \frac{x - \mu}{\sigma}. $$What does a z-score of 2.5 mean?

Accepted Answer

The value is 2.5 standard deviations above the mean.

Question 18

Which formula is used to calculate the estimated slope in a linear regression model?

Accepted Answer

$$b = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2$}$$

Comprehensive Study Guide for Introductory Statistics Final Exam

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